We imagine the four starting states shown as points in the state space of the system.
As we "jump" through the time steps so the points step through various states.
In the case shown here, the four starting states behave similarly as time goes by. This does not happen in chaotic systems.
Even though starting states might never actually reach the equilibrium state exactly, they do get closer and closer to it.
We can make long term predictions of acceptable accuracy in a system like this because we know that if we wait long enough, we will be very close to the stable equilibrium state.
Thus, we can predict that from just about any starting state, we will eventually move beyond all reasonable bounds.